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    <title>平面几何的复数解法</title>
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<ol class="theorem">
	<li>复向量 `z_1, z_2` 垂直当且仅当 `"Re"(z_1 bar z_2) = 0`;</li>
	<li>复向量 `z_1, z_2` 平行当且仅当 `"Im"(z_1 bar z_2) = 0`.</li>
</ol>

<p class="proof">
	记 `z_j = x_j + "i"y_j`, `j = 1, 2`, 则
	<span class="formula">
		`z_1 bar z_2 = (x_1 + "i"y_1)(x_2 - "i"y_2)`
		`= (x_1 x_2 + y_1 y_2) - "i"(x_1 y_2 - x_2 y_1)`.
	</span>
	由平面向量的知识知道, 两向量 `(x_1, y_1)`, `(x_2, y_2)` 垂直当且仅当
	`x_1 x_2 + y_1 y_2 = 0`, 两向量平行当且仅当 `x_1 y_2 - x_2 y_1 = 0`.
</p>

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